Obama’s top Russia adviser Mike McFaul put the problem plainly after the meeting. Despite U.S. efforts to convince the Russians the U.S does not want to threaten their security, he said, “they don’t believe us.”

At issue is Washington’s plan to site missile interceptors in Central and Eastern Europe in phases through 2020. Russia hasn’t let go of the fear that the U.S. would end up threatening Russia’s own missile arsenal, something U.S. officials say won’t happen.

Obama and Medvedev spoke on the sidelines of a two-day summit of industrialized nations here focused in part on bolstering emerging democracies in the Middle East and North Africa.

Obama said after the 90-minute meeting with Medvedev that they’d committed to working together on missile defense to find an approach that is “consistent with the security needs of both countries, that maintains the strategic balance, and deals with potential threats that we both share.”

Medvedev, however, suggested the problem wouldn’t be solved anytime soon.

“I have told my counterpart, Barack Obama, that this issue will be finally solved in the future, like, for example, in the year 2020, but we, at present, might lay the foundation for other politicians’ activities,” Medvedev said. “And this would be a sound foundation for cooperation between our two countries in the future.”

Medvedev has warned that failure to cooperate with Moscow on the missile shield could spark a new arms race.

Their meeting came in the context of an ongoing attempt to shore up relations between the U.S. and Russia, once icy but now significantly warming — to the point that Obama and Medvedev had a memorable bonding day, complete with a burger run, when the Russian president visited the U.S. less than a year ago.

But deep tensions remain. Obama’s stern expression as the leaders spoke to reporters following their meeting was in contrast to his relaxed and affable demeanor during earlier stops on his four-country Europe tour. Medvedev also appeared cool and leaned away from Obama as he talked.